VRSQRT14PD

Compute Approximate Reciprocals of Square Roots of Packed Float64 Values

stableVMJITAOTinstruction

Encodings

Operand encoding

Each mode is a value of the Op/En column above. It says which field of the encoded instruction carries each operand, in the order they are written, and whether the instruction reads it, writes it or both.

Measured cost

Description#

This instruction performs a SIMD computation of the approximate reciprocals of the square roots of the eight packed double precision floating-point values in the source operand (the second operand) and stores the packed double precision floating-point results in the destination operand (the first operand) according to the writemask. The maximum relative error for this approximation is less than 2-14.

EVEX.512 encoded version: The source operand can be a ZMM register, a 512-bit memory location, or a 512-bit vector broadcasted from a 64-bit memory location. The destination operand is a ZMM register, conditionally updated using writemask k1.

EVEX.256 encoded version: The source operand is a YMM register, a 256-bit memory location, or a 256-bit vector broadcasted from a 64-bit memory location. The destination operand is a YMM register, conditionally updated using writemask k1.

EVEX.128 encoded version: The source operand is a XMM register, a 128-bit memory location, or a 128-bit vector broadcasted from a 64-bit memory location. The destination operand is a XMM register, conditionally updated using writemask k1.

The VRSQRT14PD instruction is not affected by the rounding control bits in the MXCSR register. When a source value is a 0.0, an with the sign of the source value is returned. When the source operand is an + then +ZERO value is returned. A denormal source value is treated as zero only if DAZ bit is set in MXCSR. Otherwise it is treated correctly and performs the approximation with the specified masked response. When a source value is a negative value (other than 0.0) a floating-point QNaN_indefinite is returned. When a source value is an SNaN or QNaN, the SNaN is converted to a QNaN or the source QNaN is returned.

MXCSR exception flags are not affected by this instruction and floating-point exceptions are not reported.

Note: EVEX.vvvv is reserved and must be 1111b, otherwise instructions will #UD.

A numerically exact implementation of VRSQRT14xx can be found at https://software.intel.com/en-us/articles/reference-implementations-for-IA-approximation-instructions-vrcp14-vrsqrt14-vrcp28-vrsqrt28-vexp2.

Operation#

VRSQRT14PD (EVEX encoded versions)

(KL, VL) = (2, 128), (4, 256), (8, 512)

FOR j := 0 TO KL-1

i := j * 64

IF k1[j] OR *no writemask* THEN

             IF (EVEX.b = 1) AND (SRC *is memory*)

                  THEN DEST[i+63:i] := APPROXIMATE(1.0/ SQRT(SRC[63:0]));

                  ELSE DEST[i+63:i] := APPROXIMATE(1.0/ SQRT(SRC[i+63:i]));

             FI;

ELSE

     IF *merging-masking*                ; merging-masking

             THEN *DEST[i+63:i] remains unchanged*

             ELSE                        ; zeroing-masking

                  DEST[i+63:i] := 0

     FI;

FI;

ENDFOR;
DEST[MAXVL-1:VL] := 0

                                         Table 5-32. VRSQRT14PD Special Cases

Input value                Result value             Comments
Any denormal
X = 2-2n                   Normal                   Cannot generate overflow
X<0
X = -0                     2n
X = +0
X = +INF                   QNaN_Indefinite          Including -INF

                           -INF

                           +INF

                           +0

Intel C/C++ compiler intrinsics#

VRSQRT14PD __m512d _mm512_rsqrt14_pd( __m512d a);
VRSQRT14PD __m512d _mm512_mask_rsqrt14_pd(__m512d s, __mmask8 k, __m512d a);
VRSQRT14PD __m512d _mm512_maskz_rsqrt14_pd( __mmask8 k, __m512d a);
VRSQRT14PD __m256d _mm256_rsqrt14_pd( __m256d a);
VRSQRT14PD __m256d _mm512_mask_rsqrt14_pd(__m256d s, __mmask8 k, __m256d a);
VRSQRT14PD __m256d _mm512_maskz_rsqrt14_pd( __mmask8 k, __m256d a);
VRSQRT14PD __m128d _mm_rsqrt14_pd( __m128d a);
VRSQRT14PD __m128d _mm_mask_rsqrt14_pd(__m128d s, __mmask8 k, __m128d a);
VRSQRT14PD __m128d _mm_maskz_rsqrt14_pd( __mmask8 k, __m128d a);

SIMD Floating-Point Exceptions#

None.

Other Exceptions#

See Table 2-51, "Type E4 Class Exception Conditions."

Sources

• This instruction in the Intel manual
• Latency and throughput per microarchitecture